Chapter 5

1. Chapter 5 Series Circuits

2. Series Circuits • Two elements in a series • Connected at a single point • No other current-carrying connections at this point • A series circuitis constructed by connecting various elements in series

3. Series Circuits • Normally • Current will leave the positive terminal of a voltage source • Move through the resistors • Return to negative terminal of the source

4. Series Circuits • Current is similar to water flowing through a pipe • Current leaving the element must be the same as the current entering the element • Same current passes through every element of a series circuit

5. Series Circuits • The laws, theorems, and rules that you apply to DC circuits • Also apply to AC circuits

6. Kirchhoff’s Voltage Law (KVL) • The algebraic sum of the voltage that rises and drops around a closed loop is equal to zero • ET - V1 - V2 - V3 - ∙∙∙ - Vn = 0

7. Kirchhoff’s Voltage Law (KVL) • Another way of stating KVL is: • Summation of voltage rises is equal to the summation of voltage drops around a closed loop V1 + V2 + V3 + ∙∙∙ + Vn = ET

8. Resistors in Series • Most complicated circuits can be simplified • For a series circuit V1 + V2 + V3 = E IR1 + IR2 + IR3 = E I(R1 + R2 + R3 )= E I(R1 + R2 + R3 )= IRtotal (Note: I’s cancel)

9. Resistors in Series • Total resistance in a series circuit is the sum of all the resistor values

10. Power in a Series Circuit • Power dissipated by each resistor is determined by the power formulas: P = VI = V2/R = I2R

11. Power in a Series Circuit • Since energy must be conserved, power delivered by voltage source is equal to total power dissipated by resistors PT = P1 + P2 + P3 + ∙∙∙ + Pn

12. Voltage Sources in Series • In a circuit with more than one source in series • Sources can be replaced by a single source having a value that is the sum or difference of the individual sources • Polarities must be taken into account

13. Voltage Sources in Series • Resultant source • Sum of the rises in one direction minus the sum of the voltages in the opposite direction

14. Interchanging Series Components • Order of series components • May be changed without affecting operation of circuit • Sources may be interchanged, but their polarities can not be reversed • After circuits have been redrawn, it may become easier to visualize circuit operation

15. The Voltage Divider Rule • Voltage applied to a series circuit • Will be dropped across all the resistors in proportion to the magnitude of the individual resistors

16. The Voltage Divider Rule • Voltage dropped across each resistor may be determined by the voltage across any other resistor (or combination of resistors) by using the voltage divider rule expressed as: • The subscripts must match (x and y)

17. Voltage Divider Rule Application • If a single resistor is very large compared to the other series resistors, the voltage across that resistor will be the source voltage • If the resistor is very small, the voltage across it will be essentially zero

18. Voltage Divider Rule Application • If a resistor is more than 100 times larger than another resistor • Smaller resistor can be neglected

19. Circuit Ground • Ground • Point of reference or a common point in a circuit for making measurements • One type of grounding is chassis ground • In this type of grounding • Common point of circuit is often the metal chassis of the piece of equipment

20. Circuit Ground • Chassis ground • Often connected to Earth Ground • Earth ground • Physically connected to the earth by a metal pipe or rod

21. Circuit Ground • If a fault occurs within a circuit, the current is redirected to the earth • Voltages are often measured with respect to ground

22. Double Subscripts • For the circuit shown, we can express the voltage between any two node points (a and b) as Vab. • If a is at a higher potential than b, then Vab is positive

23. Double Subscripts • If b is at a higher potential than a, then Vab is negative • In this case, Vab would be negative

24. Double Subscripts

25. Double Subscripts • To determine correct polarity • Calculate all voltage drops across all components • Assign polarities • As you go around a circuit, add the gains and subtract the drops

26. Double Subscripts • Be sure to take the sign of the polarity on the same side of the source or element as you go around the circuit

27. Single Subscripts • In a circuit with a ground reference point • Voltages may be expressed with respect to that reference point • Va • Voltage at point a with respect to ground • Ground represents a point of zero reference potential

28. Single Subscripts • Any voltage with a single subscript is with respect to ground • This is the same as Va(0)

29. Single Subscripts • If voltages at various points in a circuit are known with respect to ground, then the voltage between points is easily determined • Vab = Va–Vb

30. Point Sources • Voltage source given with respect to ground • May be represented by a voltage at a single point (node) in the circuit • This voltage may be referred to as a point source

31. Point Sources • Voltages at these points represent voltages with respect to ground, even if ground is not shown • Point sources simplify representation of a circuit

32. Internal Resistance of Voltage Sources • Ideal sources have no internal resistance • In an ideal source • Terminal voltage does not change when the load changes • For a practical source • There is internal resistance

33. Internal Resistance of Voltage Sources • As the load changes • Drop across the internal resistance changes • Terminal voltage changes

34. Ammeter Loading Effects • An ammeter is placed in a circuit to make a measurement • Resistance will affect the circuit • Amount of loading is dependent upon the instrument and the circuit

35. Ammeter Loading Effects • If resistance of the meter is small compared to the resistance of the circuit, the loading effect will be small